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Updated: Sep 9, 2025
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Exact spectral function of one-dimensional Bose gases
Song Cheng1,2,3, Yang-Yang Chen1,4, Xi-Wen Guan5,6,7
1Institute of Modern Physics, Northwest University, Xi'an 710069, China.
National Science Review
|September 4, 2025
Summary
We precisely calculated universal many-body properties for the quantum integrable Lieb-Liniger model. Our findings confirm nonlinear Luttinger liquid theory and offer a new way to benchmark experimental observations.
Area of Science:
- Quantum Many-Body Physics
- Condensed Matter Theory
- Statistical Mechanics
Background:
- Exactly solved models are crucial for understanding strongly correlated systems.
- The quantum integrable Lieb-Liniger model is a key system for studying many-body phenomena.
- Dynamical correlation functions reveal essential properties of quantum systems.
Purpose of the Study:
- To uncover universal many-body correlated properties of the quantum integrable Lieb-Liniger model.
- To develop a high-precision method for calculating dynamical correlation functions.
- To validate theoretical predictions like nonlinear Luttinger liquid theory.
Main Methods:
- Exact calculation of dynamical correlation functions.
- Computation of form factors using a newly developed method.
- Analysis of 'relative excitations' over ground and finite temperature states.
Main Results:
- High-precision calculation of all possible relative excitations.
- Full spectral functions exhibiting unique power-law singularity behavior at the spectral threshold.
- Confirmation of the validity of nonlinear Luttinger liquid theory.
Conclusions:
- The developed method advances the theory of dynamical correlation functions towards the thermodynamic limit.
- The findings provide a benchmark for experimental observations of novel correlated properties.
- This work offers a rigorous understanding of many-body phenomena in strongly correlated quantum systems.
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